The present invention concerns a method of measuring the conductivity of a pure or ultrapure liquid, notably water.
Measuring the conductivity of a liquid is important in many industrial fields necessitating the use of ultrapure water, in particular the chemical, pharmaceutical, medical and electronics industries.
The conductivity of an aqueous solution is measured by measuring the resistance of that solution across a conductivity measuring cell that generally consists of at least two conductive material components forming electrodes.
A conductivity measuring cell is defined by its cell constant, which proportionately links the measured resistance to the conductivity of the solution. The cell constant determines the accuracy of the cell's measurements. It is therefore necessary to use cells with a low constant to measure the conductivity of an ultrapure liquid.
The conductivity measurement is affected by the geometry of the cell: the total area of the electrodes (s) and the distance between them (L). These two parameters define the cell constant k=L/s.
Conductivity is a measure of the flow of electrons through a substance. It is directly proportional to the ion concentration, the charge on the ions (valency), and their mobility. Their mobility is a function of temperature and, consequently, the measured conductivity also depends on temperature.
In theoretically pure water, the only two kinds of ions present result from the dissociation of water into H+ ions and OH− ions.
At 25° C. the theoretical conductivity of a sample of water free of ionic contamination is 0.055 μS/cm, i.e. its resistivity (resistivity is the reciprocal of conductivity) is 18.2 MΩ·cm. The resistivity of a sample is determined from the equation ρ=R/k, proportionately relating the measured resistance R of the sample and the cell constant k. Water is considered pure or ultrapure for resistivity values greater than 1 MΩ·cm.
One valuable application of water conductivity measurement is to any purification system including a water conductivity or resistivity sensor.
When measuring conductivity, it is necessary to apply a potential difference to the terminals of the electrodes immersed in the solution. A potential difference in the form of electrical pulses induces a current related to the area of the electrodes. The greater the area of the electrodes, the lower the cell constant and the commensurately more accurate the measured current. Applying a potential difference also creates resistance and capacitance phenomena throughout the electrical circuit. In particular a capacitance that is directly linked to the geometry of the cell appears at the electrode-solution interface. A small cell with a low constant induces a high capacitance.
A conductivity measuring cell immersed in water is conventionally modeled by an equivalent electrical circuit representing the resistance and capacitance effects of the system.
The conventional approach ignores or compensates capacitance and resistance effects specific to the electrodes; thus the model of the water between the electrodes becomes purely resistive or, after simplification of the model, is assigned a series capacitance.
For example, in the prior art the capacitance effects of the cell are compensated by regular calibration and by using electrodes with an area that is sufficiently large to reduce the phenomenon. One way to solve this problem is to immerse the conductivity measuring cell regularly in a solution of known resistivity and recalculate a cell constant to take account of the state of the electrodes.
Moreover, to be able to use the simplified model, and in order to reduce the risk of polarization, it is necessary to use electrical signals at a frequency that is accurately chosen as a function of the quality of the sampled water.
There are various prior art methods for determining the resistivity of a liquid. The methods described hereinafter are based on water modeled by an equivalent electrical circuit consisting of a capacitor in series with a resistor.
The central sampling method described in international patent application WO 88/01740 consists in periodically exciting the conductivity measuring cell. The output signal of the cell is analyzed over two different time periods during which the capacitance effects inherent to the cell are different. The signal obtained during the first interval is corrected for the capacitance effects on the basis of the signal differences between the two time intervals. The central sampling method and short wires eliminate from the solution equations the capacitance effects of the wires and the electrodes.
A second method for determining the resistivity of a pure or ultrapure liquid described in US patent application 2007/0024287 measures the alternating current passing through the conductivity measuring cell. The resistivity of the liquid is then calculated from the impedance difference between signals at different frequencies. An alternating electrical current at a precisely defined frequency is applied to the terminals of the conductivity measuring cell. The current is measured and the operation is repeated with a signal at a different frequency. The measured values being proportional to the impedances of the cell, the difference between the impedances obtained at the different frequencies can be used to calculate the serial capacitance and resistance effects of the sample. It is then possible, for a given frequency, to determine mathematically the resistivity of the liquid tested, including compensation of capacitance effects.
The above methods have limitations. Firstly, they limit the size of the electrodes and the cell constant. Then, to limit polarization, a conductivity measuring cell must be used at a particular frequency, as a function of a limited range of conductivity values of the liquid concerned. Finally, aging of the cell electrodes (passivity, corrosion, etc.) causes modification of the capacitance at the electrode-solution interface which cannot be controlled.
The conductivity of a small sample can be measured using a conductivity measuring cell provided with micro-electrodes, as described in French patent application No. 0655276, for example. This is because of the small size of the electrodes and because a high level of performance of the sensor, i.e. a low cell constant, is maintained. It has nevertheless been found that using micro-electrodes, thanks to their small size, can produce large capacitance effects, which can no longer be ignored. It is then necessary to revise the model of the cell in water.
As indicated above, the theoretical model of a conductivity measuring cell immersed in water is represented by an equivalent electrical circuit diagram consisting of numerous resistors and capacitors, in series or in parallel, characterizing the behavior of the components of the system. The occurrence of capacitance phenomena when using micro-electrodes must then be taken into account in the model. It is immediately apparent that adding a capacitor in series with the single resistor of the simplified model is no longer sufficient to represent the electrical behavior of the cell during tests.